1. ## inequality

when i have an inequality like this ,

$\displaystyle 0<\sqrt{13}-3<1$

If i were to find $\displaystyle (\sqrt{13}-3)^4$ , can i say that

$\displaystyle 0^4<(\sqrt{13}-3)^4<1^4 = 0<(\sqrt{13}-3)^4<1$ ??

And if the value at the side are negative , for instance

$\displaystyle -5<x<-1$
If i were find range of $\displaystyle x^2$ , am i right in saying .

$\displaystyle 25>x^2>1$

Rearrange $\displaystyle 1<x^2<25$

2. Yes, you can

3. Originally Posted by songoku
Yes, you can

THanks .

How about only one of its side is negative ?

$\displaystyle -5<x<2$

TO find $\displaystyle x^2$, do i do that this way :

$\displaystyle 25>x^2>4$

Then rearrange $\displaystyle 4<x^2<25$

4. Originally Posted by thereddevils
THanks .

How about only one of its side is negative ?

$\displaystyle -5<x<2$

TO find $\displaystyle x^2$, do i do that this way :

$\displaystyle 25>x^2>4$

Then rearrange $\displaystyle 4<x^2<25$
x = 0 satisfies $\displaystyle -5<x<2$. Does x = 0 satisfy $\displaystyle 4<x^2<25$ ....?

5. Originally Posted by mr fantastic
x = 0 satisfies $\displaystyle -5<x<2$. Does x = 0 satisfy $\displaystyle 4<x^2<25$ ....?

THanks , yeah it doesn't . But i still cant figure out how to find the range of x^2 .

6. Moral: do that as long as all pieces are positive.

7. Originally Posted by thereddevils
THanks , yeah it doesn't . But i still cant figure out how to find the range of x^2 .
The range of $\displaystyle f(x)= x^2$ is the set of all non-negative numbers.

8. Originally Posted by thereddevils
How about only one of its side is negative ?

$\displaystyle -5<x<2$

TO find $\displaystyle x^2$, do i do that this way :

math]25>x^2>4 [/tex]

Then rearrange $\displaystyle 4<x^2<25$
Originally Posted by mr fantastic
x = 0 satisfies $\displaystyle -5<x<2$. Does x = 0 satisfy $\displaystyle 4<x^2<25$ ....?
Originally Posted by thereddevils
THanks , yeah it doesn't . But i still cant figure out how to find the range of x^2 .
Draw a graph of y = x^2 for -5 < x < 2. Now look at the range of values of x^2.